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Bas_tet [7]
2 years ago
12

I really need help rn T_T plz help me out!

Mathematics
1 answer:
pshichka [43]2 years ago
4 0

Answers:

  • The lengths of sides PQ and RS are <u>   13   </u>
  • The lengths of sides QR and SP are <u>   </u><u>20  </u>

This is a 13 by 20 rectangle.

============================================================

Explanation:

Refer to the drawing below.

Let x be the length of side SP. Since we're dealing with a rectangle, the opposite side is the same length. Side QR is also x units long.

We're told that RS = SP - 7 which is the same as saying RS = x-7

We also know that PQ = x-7 as well because PQ is opposite side RS.

In short, we have these four sides in terms of x

  • PQ = x-7
  • QR = x
  • RS = x-7
  • SP = x

as shown in the drawing. The four sides add up to the perimeter of 66.

PQ+QR+RS+SP = perimeter

PQ+QR+RS+SP = 66

(x-7)+x+(x-7)+x = 66

4x-14 = 66

4x = 66+14

4x = 80

x = 80/4

x = 20

Use this x value to find the unknown side lengths.

  • PQ = x-7 = 20-7 = 13
  • QR = x = 20
  • RS = x-7 = 20-7 = 13
  • SP = x = 20

In short, this is a 13 by 20 rectangle.

-----------------

Check:

perimeter = side1+side2+side3+side4

perimeter = PQ+QR+RS+SP

perimeter = 13+20+13+20

perimeter = 33+33

perimeter = 66

The answer is confirmed.

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