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The area of rectangle ABCD
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22 Dec 2022, 11:20
22 Dec 2022, 11:20
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Question Stats:
70% (00:36) correct
29% (01:13) wrong based on 37 sessions
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Quantity A |
Quantity B |
The area of rectangle ABCD |
The area of Triangle STU |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Re: The area of rectangle ABCD
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04 Jan 2023, 07:22
04 Jan 2023, 07:22
Expert Reply
OE
The formula for the area of rectangle ABCD = l x w = 6 x 4 = 24. To figure out the area of triangle STU, use the Pythagorean theorem to solve for ST (the base of the triangle): \(6^2 + ST^2 = 10^2\). Therefore, \(ST^2 = 64\) and ST = 8. Alternatively, you could recognize that triangle STU is a 6 -8-10 triangle. The area of a triangle is given by the formula 1/2 b*h, which is 1/2 *8*6=24
The formula for the area of rectangle ABCD = l x w = 6 x 4 = 24. To figure out the area of triangle STU, use the Pythagorean theorem to solve for ST (the base of the triangle): \(6^2 + ST^2 = 10^2\). Therefore, \(ST^2 = 64\) and ST = 8. Alternatively, you could recognize that triangle STU is a 6 -8-10 triangle. The area of a triangle is given by the formula 1/2 b*h, which is 1/2 *8*6=24
The area of rectangle ABCD
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05 Feb 2024, 07:13
05 Feb 2024, 07:13
1
Quantity A = Area of Rectangle ABCD \(= 6 \times 4 = 24\)
Quantity B = Area of Triangle = \(\frac{1}{2} \times Base \times Height = \frac{1}{2} \times 8 \times 6 = \frac{1}{2} \times 48 = 24\)
(since 10 is the hypotenuse,10 and 6 constitute twice the Pythagorean triplet 3,4 and 5. Therefore, the base will be 8.)
BOTH quantities are EQUAL.
The answer is C.
Quantity B = Area of Triangle = \(\frac{1}{2} \times Base \times Height = \frac{1}{2} \times 8 \times 6 = \frac{1}{2} \times 48 = 24\)
(since 10 is the hypotenuse,10 and 6 constitute twice the Pythagorean triplet 3,4 and 5. Therefore, the base will be 8.)
BOTH quantities are EQUAL.
The answer is C.
