A rectangular photo frame has a perimeter of 46 cm and a diagonal of 17 cm. What is its area?

60 cm²Correct answerYour answer120 cm²Correct answerYour answer132.25 cm²Correct answerYour answer240 cm²Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Let the sides be l and b. Then $l + b = 46 \div 2 = 23$ and $l^2 + b^2 = 17^2 = 289$ .
$(l + b)^2 = l^2 + b^2 + 2lb$ , so $529 = 289 + 2lb$ , giving $2lb = 240$ .
Area = $lb = 120$ cm². (The sides are 15 cm and 8 cm.)

Worth noting

240 is 2lb; halve it. 132.25 cm² assumes the frame is a square with side 11.5 cm, but then the diagonal would not be 17 cm.

Ten questions from Mensuration: Areas and Volumes, at your own pace.

Ten questions from Mensuration: Areas and Volumes, at your own pace.

Explanation