A plot is in the shape of a right-angled triangle whose shorter sides measure 78.8 meters and 62.4 meters respectively.

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

A plot is in the shape of a right-angled triangle whose shorter sides measure 78.8 meters and 62.4 meters respectively.

by Vincen » Fri Jun 19, 2020 2:42 am

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A plot is in the shape of a right-angled triangle whose shorter sides measure 78.8 meters and 62.4 meters respectively. If an insect takes 1.79 minutes to cover a distance of 100 inches, what is the approximate time that it will take to return to its starting point after covering the entire perimeter of the plot in one direction? (1 meter is approximately 39.37 inches)

A. 24 seconds
B. 4 minutes
C. 17 minutes
D. 3 hours
E. 290 hours

[spoiler]OA=D[/spoiler]

Source: e-GMAT

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Source: Beat The GMAT — Problem Solving | Fri Jun 19, 2020 2:42 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pm; Followed by:5 members

Re: A plot is in the shape of a right-angled triangle whose shorter sides measure 78.8 meters and 62.4 meters respective

by deloitte247 » Sat Jun 20, 2020 11:14 am

Let opposite = o = 78.8 metres
Let adjascent = a = 62.4 metres
Let hypotenuse = h = ??
Given that an insect covers 100 inches in 1.79 minutes and 1 meter = 39.37 inches
$$o=39.37\cdot78.8=3102.36\approx3102\ inches$$
$$a=39.37\cdot62.4=2456.69\approx2457\ inches$$
$$clo\sin g\ pythagoras,\ h=\sqrt{o^2+a^2}$$
$$\ h=\sqrt{\left(3102\right)^2+\left(2457\right)^2}$$
$$\ h=\sqrt{9622404+6036849}$$
$$\ h=\sqrt{15,659,253}$$
$$\ h=3957.18\approx3957\ inches$$
Perimeter of a triangle = o + a + h
= 3102 + 2457 + 3957
=9516 inches
Insect covers 100 inches in 1.79 minutes
It will cover 9516 inches in t
$$t=\frac{9516\cdot1.79}{100}$$
$$t=170.34\approx170\min utes$$
If it takes 170 minutes to cover the perimeter then it will take 170 minutes to get back to the starting point
Converting 170 minutes to hours:
$$=>\frac{170}{60}=2.83\approx3hours$$
$$Answer\ =\ D$$