Question

please solve in 2 minutes
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Answer 1

$\bf\huge\ Question:-$

please solve in 2 minutes

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$\bf\huge\ Answer:-$

your answer is 10

Answer 2

Step-by-step explanation:

There are many ways to solve the problem, such as using coordinate geometry. I will present a solution using similar triangles.

Let AB = h, and AD = s. Then AG = GD = s/2 and BE = EF = FG = s/3.

To begin, triangles BHE and DHG are similar. Since BE/GD = (s/3)/(s/2) = 2/3, the height of the smaller triangle BHE will also be 2/3 of the height of the larger triangle DHG.

We then have x + (2/3)x = h so x = (3/5)h.

Next, triangles BIF and DIG are similar. Since BF/GD = (2s/3)/(s/2) = 4/3, the height of the larger triangle will be 4/3 of the smaller triangle.

We then have y + (4/3)y = h so y = (3/7)h.

We can then calculate the area of HIG as follows:

Area(HIG) = Area(DHG) – Area(DIG)

Area(HIG) = (1/2)(3h/5)(s/2) – (1/2)(3h/7)(s/2)

Area(HIG) = 3hs/70

Since the area of ABCD = 10, we have hs = 10. Thus we have:

Area(HIG) = 3(10)/70

Area(HIG) = 3/7

What’s remarkable is the answer is determined by the area of ABCD,so the area of the triangle is same for all rectangles with an area of 10.