Question

Given the diagram below find the value of x if the area is 78 square meters

Answer 1

x = 6 meters

Explanation:

The formula for area of a rectangle is simply A =lw so plugging what we're given into this equation, we use 78 = x(x + 7) to find x

`78=x(x+7)\\78=x^2+7x\\0=x^2+7x-78`

We can find the solution for x by factoring.

We essentially need two numbers whose product is -78 and whose sum is 7.

13 * -6 = -78

13 - 6 = 7

Thus, if we write the equation in factored form where 13 and -6 are our two factors, we have 0 = (x + 13)(x - 6).

Thus, our two solutions are x = -13 and x = 6. However, because you cannot have negative measures, our solution is simply x = 6 meters.