Jordan is designing a picture frame for a poster. The perimeter of the frame is 80cm80\operatorname{cm}. The length is 12cm12\operatorname{cm} longer than its width. Identify the dimensions of this poster.

L=26cm⁡L=26\operatorname{cm} and w=14cm⁡w=14\operatorname{cm}

Jordan is designing a picture frame for a poster. The perimeter of the frame is 80 cm 80\operatorname{cm} . The length is 12 cm 12\operatorname{cm} longer than its width. Identify the dimensions of this poster.

For this problem, Jordan is designing a picture frame for a poster. The perimeter of the frame will be 80 centimeters, and we know that the length needs to be 12 centimeters longer than the width. So let's identify the dimensions of this poster. To help us solve this problem, let's first draw a picture. Posters are generally a rectangular shape. So let's draw a rectangle. And what do we know about this poster? We know that the perimeter is 80 centimeters. So we can write perimeter p equals 80. We also know that the length is 12 centimeters longer than its width. So we know that this poster has some length, which we'll call L, and some width, which we'll call w. Now that length is 12 centimeters longer than the width. So let's go ahead and build our equation to model this problem. We need something that relates all three of our quantities, perimeter, length, and width. And we can do that with the perimeter formula. Perimeter is length plus length plus width plus width, which simplifies to two l plus two w. Now we already know the value for P. We know that P equals 80, so we can plug that in. But we still have L and W, which is more variables than we know how to solve for. But we do know the relationship between these two variables. We know that the length is 12 centimeters longer than the width, And we can write that as length L equals our width plus 12 centimeters. So using that we can substitute in w plus 12 in for L in our equation, And we get 80 equals two times w plus 12 plus two w. So now we have only one variable and we're ready to solve our equation. We can distribute in the two and simplify and we get 80 equals two w plus 24 plus another two w. Combining like terms, we have 80 equals four w plus 24. Now we're ready to isolate w by subtracting 24 from both sides. We have 56 equals four w, and dividing both sides by four, we get w equals 14. So that's one of the dimensions of our poster. In order to find the other one length, we simply need to take our value for w and plug it back into our length equation above. And we get length is equal to 14 plus 12. So our length equals 26. And lastly, we can check our answer by plugging in w, l and p back into that equation that we built to make sure everything checks out. So we get 80 equals two times our length of 26 plus two times our width of 14. So 80 equals 52 plus 28 and indeed 80 equals 80. So we can feel confident that our answer here is correct.

Jordan is designing a picture frame for a poster. The perimeter of the frame is 80cm⁡80\operatorname{cm}. The length is 12cm⁡12\operatorname{cm} longer than its width. Identify the dimensions of this poster.

L=26cm⁡L=26\operatorname{cm} and w=14cm⁡w=14\operatorname{cm}

L=46cm⁡L=46\operatorname{cm} and w=34cm⁡w=34\operatorname{cm}

L=23cm⁡L=23\operatorname{cm} and w=17cm⁡w=17\operatorname{cm}

L=52cm⁡L=52\operatorname{cm} and w=28cm⁡w=28\operatorname{cm}

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Multiple Choice

Jordan is designing a picture frame for a poster. The perimeter of the frame is $80 cm$ . The length is $12 cm$ longer than its width. Identify the dimensions of this poster.

$L equals 46 cm$ and $w equals 34 cm$

$L equals 23 cm$ and $w equals 17 cm$

$L equals 52 cm$ and $w equals 28 cm$

$L equals 26 cm$ and $w equals 14 cm$

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Verified step by step guidance

Let the width of the poster be represented by the variable $w$ (in cm).

Since the length is 12 cm longer than the width, express the length as $L = w + 12$.

Recall the formula for the perimeter of a rectangle: $P = 2L + 2w$. Substitute the given perimeter value and the expression for $L$ into this formula: \$80 = 2(w + 12) + 2w$.

Simplify and solve the equation for $w$: first expand to get \$80 = 2w + 24 + 2w$, then combine like terms to get $80 = 4w + 24$, and finally isolate $w$ by subtracting 24 from both sides and dividing by 4.

Once you find $w$, substitute it back into $L = w + 12$ to find the length $L$. These values will give you the dimensions of the poster.

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Jordan is designing a picture frame for a poster. The perimeter of the frame is 80cm80\(\operatorname{cm}\). The length is 12cm12\(\operatorname{cm}\) longer than its width. Identify the dimensions of this poster.

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Jordan is designing a picture frame for a poster. The perimeter of the frame is $80 cm$ . The length is $12 cm$ longer than its width. Identify the dimensions of this poster.