Question

Please help, having trouble with geometry word problems. Tysm if you do :)

Answer 1

Hi!

So let's start with some variables.

w is width

L is length.

The length is 4 less than 5 times the width. Let's put that into an equation.

L = 5w - 4

The perimeter is 76.

The perimeter is L + L + w + w or

perimeter = 2L + 2w.

Which means that 1/2 of the perimeter = L + w.

We know the perimeter is 76, so half of 76 is 38.

38 = L + W.

Let's put length in terms of width and plug in the previous equation.

38 = 5w - 4 + w

Add the same variables

38 = 6w - 4

simplify

42 = 6w

w = 7

And plug that into the length equation that we had above to get

L = 35 - 4

L = 31

The correct answer is C: 7, 31

Answer 2

Answer:

1. C. 7, 31 cm

2. A. 43°, 137°

Step-by-step explanation:

1.

A. 14+14+66+66=160 (incorrect)

B. 7+7+27+27= 68 (incorrect)

C. 7+7+31+31= 76 (correct)

D. 7+7+39+39= 92 (incorrect)

For this question, they give you a red herring. Since it's a multiple choice question, you can just add their length and width and see if they add up to 76. Only C. 7, 31 cm dimensions add up to have a perimeter of 76.

2.

Supplementary angles add up to 180°

The formula is x° × 5 = y° × 2 - 59

A. 43° × 5 = 137° × 2 - 59 (correct)

B. 41° × 5 ≠ 139° × 2 - 59 (incorrect)

C. 39° × 5 ≠ 141° × 2 - 59 (incorrect)

D. 37° × 5 ≠ 143° × 2 - 59 (incorrect)

For this question, you can't add up the angle measurements because they all equal 180°. Since it's a multiple choice question, you can just try them and see which one fits. Only A. 43°, 137° has angles that fit our formula.