David told Jen, "Write three two-digit numbers. I'll add three more and give you the sum right away." Jen wrote 53, 42, and 31.
1 answer:
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Answer:
No
Step-by-step explanation:
Let's test these values using the Pythagorean Theorem.
a^2+b^2=c^2
where a and b are the legs and c is the hypotenuse.
a and b are the legs, or the shorter sides. 5 and 12 are the shorter sides, so they are a and b.
c is the hypotenuse, or the longest side. 14 is the longest side, so it is c.
5^2+12^2=14^2
Evaluate all the exponents
25+144=196
Add 25 and 144
169=196
169196
169 is not equal to 196, so 5, 12 and 14 cannot be a Pythagorean Triple
The squares are shown in the attached picture.
As you can see, JC is half the diagonal of ABCD and JH is half the diagonal of EFGH.
In order to find the area of the shaded figure, we need to subtract the area of the white square (EFGH) from the area of the big square (ABCD).
The area of a square know the diagonal is given by the formula:
A = d² ÷ 2
A(ABCD) = (2×JC)² ÷ 2
= (2×9)² ÷ 2
= 162 cm²
A(EFGH) = (2×JH)² ÷ 2
= (2×4)² ÷ 2
= 32 cm²
Therefore:
A = A(ABCD) - <span>A(EFGH)
= 162 - 32
= 130 cm</span>²
The area of the shaded region is 130 cm².
As you can see, JC is half the diagonal of ABCD and JH is half the diagonal of EFGH.
In order to find the area of the shaded figure, we need to subtract the area of the white square (EFGH) from the area of the big square (ABCD).
The area of a square know the diagonal is given by the formula:
A = d² ÷ 2
A(ABCD) = (2×JC)² ÷ 2
= (2×9)² ÷ 2
= 162 cm²
A(EFGH) = (2×JH)² ÷ 2
= (2×4)² ÷ 2
= 32 cm²
Therefore:
A = A(ABCD) - <span>A(EFGH)
= 162 - 32
= 130 cm</span>²
The area of the shaded region is 130 cm².