In , the side lengths are , and . A point on is such that . The line through drawn…

MATHEMATICS · Multi-part · GCSE · Mathematics · Ratio and Proportion · Ratio and Proportion

Problem

\triangle XYZ

, the side lengths are

XY = 15\,\text{cm}

XZ = 24\,\text{cm}

and

YZ = 30\,\text{cm}

. A point

P

XY

is such that

XP = 6\,\text{cm}

. The line through

P

drawn parallel to

XZ

meets

YZ

Q

. A point

R

XZ

is chosen so that

XR = 9\,\text{cm}

. The line through

R

drawn parallel to

XY

meets

YZ

S

. (i) Determine

YQ

and

QZ

. (ii) Calculate

YS

and

SZ

. (iii) Find

QS

and hence obtain the ratio of the area of trapezium

PQRS

to the area of

\triangle XYZ