Question

The diagram below shows the rectangle PLUM.

P
L
8
M
U
Find the area of rectangle PLUM.

Answer 1

Answer: 75

Step-by-step explanation: Khan Academy

Answer 2

Area of rectangle PLUM = 75.00 square units

Explanation:

Since diagonal of rectangle divides the rectangle into two equal triangles,

Therefore, area of the rectangle PLUM = 2× area of triangle PLM

By the mean proportional theorem,

In ΔPLM,

AP² = AM × AL

6² = AM × 8

AM =
`(36)/(8)`

AM = 4.5 units

Area of PLM =
`(1)/(2)(\text{Base})(\text{height})`

=
`(1)/(2)(ML)(AP)`

=
`(1)/(2)(8 + 4.5)(6)`

= 12.5 × 3

= 37.5 units²

Now area of rectangle PLUM = 2×37.5 = 75 units²

Therefore, area of the rectangle is 75.00 square units.