The longest side of triangle GHI is GI, which measures 26 cm.

Perimeter = GH + HI + GI = 10 + 24 + 26 = 60 cm.

Since the sides are in the ratio 3:4:5, it follows the Pythagorean theorem, indicating it is a right-angled triangle.

Using the Pythagorean theorem, JL = √(KL² - JK²) = √(20² - 15²) = √(400 - 225) = √175 = 12.25 cm.

Using Pythagoras theorem: JL = √(KL² - JK²) = √(20² - 15²) = √(400 - 225) = √175 = 12 cm.

Semi-perimeter = (JK + KL + JL) / 2 = (15 + 20 + 25) / 2 = 30 cm.

Semi-perimeter = (JK + KL + JL) / 2 = (15 + 20 + 25) / 2 = 30 cm.

Since 15² + 20² = 25² (225 + 400 = 625), triangle JKL is a right-angled triangle.

Since 5² + 12² = 13² (25 + 144 = 169), triangle JKL is a right-angled triangle.

Using the Pythagorean theorem, 8² + 15² = 64 + 225 = 289 = 17². Hence, it is a right-angled triangle.

Using Heron's formula, s = (10 + 24 + 26) / 2 = 30. Area = √(30(30-10)(30-24)(30-26)) = √(30*20*6*4) = √(4800) = 120 cm².

Perimeter = PQ + QR + PR = 8 + 6 + 10 = 24 cm.

Semi-perimeter = (PQ + QR + PR) / 2 = (8 + 6 + 10) / 2 = 12 cm.

Semi-perimeter = (PQ + QR + PR) / 2 = (8 + 6 + 10) / 2 = 12 cm.

In an isosceles right triangle, the sides opposite the 45-degree angles are equal. Therefore, XY = XZ / √2 = 10 / √2 = 5√2 cm.

In an isosceles triangle with angles 45 degrees, the sides opposite these angles are equal, hence the ratio is 1:1.

In an isosceles triangle with angles 45-45-90, the sides opposite the equal angles are equal, hence the ratio is 1:1.

Semi-perimeter s = (XY + YZ + XZ)/2 = (12 + 16 + 20)/2 = 24 cm.

The longest side in triangle XYZ is XZ, which measures 17 cm.

Circumference = 2πr => r = circumference / (2π) = 31.4 / (2 * 3.14) = 5 cm

Using Heron's formula, s = (5 + 12 + 13)/2 = 15. Area = √[s(s-a)(s-b)(s-c)] = √[15(15-5)(15-12)(15-13)] = √[15*10*3*2] = √[900] = 30 cm².

Using the Pythagorean theorem, 7^2 + 24^2 = 49 + 576 = 625 = 25^2. Therefore, triangle ABC is a right triangle.

This is a right triangle. Area = 1/2 * base * height = 1/2 * 5 * 12 = 30 cm².

In an equilateral triangle, all sides are equal. Therefore, each side = Perimeter / 3 = 36 / 3 = 12 cm.

If r is the original radius, new radius = 1.5r. Area increases from πr² to π(1.5r)² = 2.25πr². Percentage increase = (2.25 - 1) × 100% = 125%.

The distance between the centers of two externally tangent circles is the sum of their radii: 3 + 4 = 7 cm.

Distance between centers = r1 + r2 = 3 cm + 5 cm = 8 cm.

The distance between the centers of two externally tangent circles is the sum of their radii: 3 + 4 = 7 cm.

Distance between centers = r1 + r2 = 5 cm + 3 cm = 8 cm.

If two lines are perpendicular, the sum of their angles is 90 degrees. Therefore, if one line makes an angle of 30 degrees with the horizontal, the other line must make an angle of 90 - 30 = 60 degrees with the horizontal.