BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

If the hypotenuse of isosceles right triangle ABC has the same length as the height of equilateral triangle DEF...

Expert replies
by AAPL » Wed Jan 13, 2021 4:19 pm

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty

Manhattan Prep

If the hypotenuse of isosceles right triangle ABC has the same length as the height of equilateral triangle DEF, what is the ratio of a leg of triangle ABC to a side of triangle DEF?

A. \(\sqrt{2}/2\)
B. \(\sqrt{3}/2\)
C. \(\sqrt{3}/(2\sqrt{2})\)
D. \(\sqrt{2}/\sqrt{3}\)
E. \(\dfrac{3}{2}\)

OA C
Join the discussion
Source: — Problem Solving |

AAPL wrote:
Wed Jan 13, 2021 4:19 pm
Manhattan Prep

If the hypotenuse of isosceles right triangle ABC has the same length as the height of equilateral triangle DEF, what is the ratio of a leg of triangle ABC to a side of triangle DEF?

A. \(\sqrt{2}/2\)
B. \(\sqrt{3}/2\)
C. \(\sqrt{3}/(2\sqrt{2})\)
D. \(\sqrt{2}/\sqrt{3}\)
E. \(\dfrac{3}{2}\)

OA C
Solution:

Let the hypotenuse of isosceles right triangle ABC be 1; thus, the height of equilateral triangle DEF is 1 also. Furthermore, a leg of triangle ABC is 1/√2, and a side of triangle DEF is 1/√3 x 2 = 2/√3. Therefore, the ratio is (1/√2) / (2/√3) = 1/√2 x √3/2 = √3/(2√2).

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Join the discussion