Question

rectangular carpet has an area 60 sq m. its diagonal n longer side together equals 5 times the shorter side. find the length of the carpet

Answer 1

rectangular carpet has an area 60 sq m. its diagonal n longer side together equals 5 times the shorter side. find the length of the carpet

1) Let's write the formula defining area of rectangle:

$$S = ab (1)$$

2) Consider the triangle ABC:

Use Pythagorean Theorem:

$$c^2 = a^2 + b^2 (2)$$

3) According to the task:

$$a + c = 5b \quad \text{---} \quad c = 5b - a$$

4) Use formula from step 2:

$$\begin{array}{l} (5b - a)^2 = a^2 + b^2 \\ 25b^2 + a^2 - 10ab - a^2 - b^2 = 0 \\ 24b^2 - 10ab = 0 \\ \end{array}$$

5) Use formula from step1:

$$\begin{array}{l} S = ab \quad \text{---} \quad 60 = ab \quad \text{---} \quad a = 60/b (4) \\ 24b^2 - 600 = 0 \\ 24b^2 = 600 \\ b^2 = 25 \\ b = 5 \text{ (shorter side)} \\ \end{array}$$

Use(formula (4)):

$$a = 60/5 = 12 \text{ (longer side)}$$

Answer: shorter side B equals to 5, longer side A equals to 12.