Question

The diagram below shows the rectangle PLUM.

Answer 1

Answer:

Area of rectangle PLUM = 75.00 square units

Step-by-step 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 = $\frac{36}{8}$

AM = 4.5 units

Area of PLM = $\frac{1}{2}(\text{Base})(\text{height})$

                     = $\frac{1}{2}(ML)(AP)$

                     = $\frac{1}{2}(8 + 4.5)(6)$

                     = 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.