JAMB 1993 · UME · Q35

Plane mensuration

In the figure, the area of the square $PQRS$ is $100\text{ cm}^2$ . If the ratio of the area of the square $TUYS$ to the area of the square $XQVU$ is $1 : 16$ , find $YR$ .

Worked solution (try it first)

$PQRS$ has area 100 cm², so its side is 10 cm.
The areas of the small squares are in the ratio $1 : 16$ , so their sides are in the ratio $1 : 4$ .
Call them $a$ and $4a$ .
Along $SR$ : $SY + YR = a + 4a = 10$ , so $a = 2$ .
$YR$ is a side of the big square $XQVU$ : $YR = 4a = 8$ cm, option C.

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