Question

3 multiple answer 1 point which of these rectangles has the same area as the triangle? choose all the correct answers. a an 11 cm - by - 13 cm rectangle b a 21 cm - by - 6 cm rectangle c an 18 cm - by - 7 cm rectangle d a 12 cm - by - 8 cm rectangle e a 14 cm - by - 9 cm rectangle

Explanation:

Step1: Calculate area of the triangle

The area formula for a triangle is $A=\frac{1}{2}\times base\times height$. Here, base = 21 cm and height is the perpendicular height. Let's assume the perpendicular height is the one corresponding to the base of 21 cm. So $A_{triangle}=\frac{1}{2}\times21\times12 = 126$ $cm^{2}$.

Step2: Calculate areas of rectangles

• For rectangle A with length $l = 11$ cm and width $w=13$ cm, $A_{A}=11\times13 = 143$ $cm^{2}$.
• For rectangle B with length $l = 21$ cm and width $w = 6$ cm, $A_{B}=21\times6=126$ $cm^{2}$.
• For rectangle C with length $l = 18$ cm and width $w = 7$ cm, $A_{C}=18\times7 = 126$ $cm^{2}$.
• For rectangle D with length $l = 12$ cm and width $w = 8$ cm, $A_{D}=12\times8=96$ $cm^{2}$.
• For rectangle E with length $l = 14$ cm and width $w = 9$ cm, $A_{E}=14\times9 = 126$ $cm^{2}$.

Answer:

B. a 21 cm - by - 6 cm rectangle
C. an 18 cm - by - 7 cm rectangle
E. a 14 cm - by - 9 cm rectangle