Question

In the diagram, PQRS is a trapezium and TUV is an equilateral triangle. The perimeter of trapezium PQRS is equal to the perimeter of triangle TUV.

find the value of Y

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Answer 1

y = 12

Explanation:

The first step is to determine the perimeter of triangle TUV. We know side UV has a length of 20 cm and that the triangle is equilateral, so all sides have the same length. Thus the perimeter of the triangle must be 20 cm * 3 = 60 cm

The perimeter of PQRS is the sum of the lengths of sides PQ, QR, RS, and SP in cm.

PQ = y + 6

QR = 9 (given in diagram)

RS = 2y

SP = 9 (the diagram shows that it has the same length as QR)

Together they must add up to 60 cm to match the perimeter of the triangle, so:

PQ + QR + RS + SP = 60

(y + 6) + 9 + 2y + 9 = 60

3y + 24 = 60

3y = 36

y = 12