Question

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 the area of the triangle

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\). Here, the base of the triangle is \(21\) cm and the height is \(12\) cm. So, \(A_{triangle}=\frac{1}{2}\times21\times12\).

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Step2: Calculate the area of each rectangle

• For rectangle A (11 cm - by - 13 cm):

The formula for the area of a rectangle is \(A = length\times width\). So, \(A_{A}=11\times13 = 143\space cm^{2}\)

• For rectangle B (21 cm - by - 6 cm):

\(A_{B}=21\times6=126\space cm^{2}\)

• For rectangle C (18 cm - by - 7 cm):

\(A_{C}=18\times7 = 126\space cm^{2}\)

• For rectangle D (12 cm - by - 8 cm):

\(A_{D}=12\times8=96\space cm^{2}\)

• For rectangle E (14 cm - by - 9 cm):

\(A_{E}=14\times9 = 126\space cm^{2}\)

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