Question

1. find the missing lengths of the triangles below. if necessary, round answers to 1 decimal place.

Explanation:

Step1: Apply Pythagorean theorem for first triangle

For the triangle with sides 3.4 cm and 9 cm, by the Pythagorean theorem $a=\sqrt{3.4^{2}+9^{2}}$.
$a=\sqrt{11.56 + 81}=\sqrt{92.56}\approx9.6$ cm.

Step2: Apply Pythagorean theorem for second triangle

For the triangle with sides 8 cm and 17 cm, $b=\sqrt{17^{2}-8^{2}}$.
$b=\sqrt{(17 + 8)(17 - 8)}=\sqrt{25\times9}=\sqrt{225}=15$ cm.

Step3: Apply Pythagorean theorem for third triangle

For the triangle with sides 6 cm and 10 cm, $c=\sqrt{10^{2}-6^{2}}$.
$c=\sqrt{(10 + 6)(10 - 6)}=\sqrt{16\times4}=\sqrt{64}=8$ cm.

Step4: Apply Pythagorean theorem for fourth triangle

For the triangle with sides 1.9 cm and 2.4 cm, $d=\sqrt{1.9^{2}+2.4^{2}}$.
$d=\sqrt{3.61+5.76}=\sqrt{9.37}\approx3.1$ cm.

Step5: Apply Pythagorean theorem for fifth triangle

For the triangle with sides 15 cm and 9 cm, $e=\sqrt{15^{2}-9^{2}}$.
$e=\sqrt{(15 + 9)(15 - 9)}=\sqrt{24\times6}=\sqrt{144}=12$ cm.

Step6: Apply Pythagorean theorem for sixth triangle

For the triangle with sides 16 cm and 20 cm, $f=\sqrt{20^{2}-16^{2}}$.
$f=\sqrt{(20 + 16)(20 - 16)}=\sqrt{36\times4}=\sqrt{144}=12$ cm.

Answer:

$a\approx9.6$ cm, $b = 15$ cm, $c = 8$ cm, $d\approx3.1$ cm, $e = 12$ cm, $f = 12$ cm