A rectangle is 3 feet longer than it is wide. Write the equation for the perimeter of the rectangle.

1 answer:

4 0

Let x be the width of the rectangle
Therefore length=3+x
Thus the formula to find the perimeter of the rectangle is:2(3+x+x)

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Olin [163]

Answer:

m<SQP=124°

Step-by-step explanation:

Hi there!

We're given ΔQRS, the measure of <R (90°), and the measure of <S (34°)

we need to find m<SQP (given as x+72°)

exterior angle theorem is a theorem that states that an exterior angle (an angle on the OUTSIDE of a shape) is equal to the sum of the two remote interior angles (the angle OUTSIDE of a shape will be equal to the sum of 2 angles that are OPPOSITE to that angle).

that means that m<SQP=m<R+m<S (Exterior angle theorem)

substitute the known values into the equation

x+72°=90°+34° (substitution)

combine like terms on both sides

x+72°=124° (algebra)

subtract 72 from both sides

x=52° (algebra)

however, that's just the value of x. Because m<SQP is x+72°, add 52 and 72 together to get the value of m<SQP

m<SQP=x+72°=52°+72°=124° (substitution, algebra)

Hope this helps!

4 0

3 years ago