Question

find the value of a.
3 m

a
a
14 m
perimeter = 37 meters
a = meters
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work it out
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Explanation:

Step1: Recall perimeter formula

The perimeter of a trapezoid (or any polygon) is the sum of all its side lengths. For this trapezoid, the sides are \(3\) m, \(14\) m, and two sides of length \(a\) (since the two non - parallel sides are equal as per the diagram). So the perimeter \(P = 3+14 + a+a\).

Step2: Substitute the known perimeter

We know that the perimeter \(P = 37\) meters. So we can set up the equation: \(3 + 14+2a=37\).
First, simplify the left - hand side: \(17 + 2a=37\).
Then, subtract \(17\) from both sides of the equation: \(2a=37 - 17\).
Calculate \(37-17 = 20\), so \(2a = 20\).

Step3: Solve for \(a\)

Divide both sides of the equation \(2a = 20\) by \(2\): \(a=\frac{20}{2}=10\).

Answer:

10